In OFDM systems, blocks of data are converted from the frequency domain to the time domain using an inverse fast Fourier transform function (IFFT). Effectively, one data element is carried on each of one of a large number of sub-carriers which are closely but orthogonally spaced.
An example of this is shown in FIG. 1 where three OFDM symbols are indicated at 10,12,14. Symbol 10 is referred to as IFFTk−1, symbol 12 is IFFTk and symbol 14 is IFFTk+1. These OFDM symbols 10,12,14 constitute the transmitter output 15. These are transmitted over the wireless channel which in the illustrated example is shown to have a channel impulse response 16 or, equivalently a sampled channel response 20. The effect of transmitting over this channel is that the transmitter output 15 is linearly convoluted with the multi-path channel. This is indicated symbolically at 18. Then, at a receiver, three OFDM symbols 22,24,26 are received. These will again contain the IFFTk−1, IFFTk, and IFFTk+1 respectively. However, due to the multi-path channel IFFTk−1 will result in inter-symbol interference in IFFTk. More specifically, the OFDM ISIk−1 28 is the inter-symbol interference which is caused by IFFTk−1 in IFFTk, and similarly OFDM ISIk 30 is the inter-symbol interference caused by IFFTk 24 in IFFTk+1 26. This inter-symbol interference makes the first part of each OFDM symbol effectively useless for transmitting information. Various approaches have been employed to combat this problem. FIG. 2 shows a first known approach. With this approach, a guard interval is left between each pair of consecutive OFDM symbols, and a prefix for each OFDM symbol is formed by copying a part of the data (the so called Identical Cyclic Prefix), typically from the end of the OFDM symbol. In the example of FIG. 2, shown are three OFDM symbols 40,42,44 represented by IFFTk−1, IFFTk and IFFTk+1. The latter part of IFFTk is shown copied into the prefix 46 and the latter part of IFFTk+1 44 is copied into a second prefix 48. Now, the ISI due to preceding symbols will only interfere with the prefix, and the actual OFDM symbol will be left undistorted. This can be seen in the figure where OFDM ISIk−1 50 is shown to overlap with the prefix 46 upon reception, and OFDM ISIk 52 is shown to overlap with prefix 48 upon reception. An important side benefit of this approach is that by copying the end part of each IFFT to the prefix, the convolution which occurs between the transmitter output and the multi-path channel becomes mathematically a cyclic convolution rather than a standard linear convolution after the removal of the corresponding prefix part in the receiver end. A cyclic convolution has some important advantages when it comes to performing channel estimation and compensation and multipath cancellation. The disadvantage of this Identical cyclic Prefix method is the power and bandwidth used by this prefix is a pure overload.
FIG. 3 shows a second known approach to dealing with the problem. In this case, rather than transmitting a prefix containing a copy of part of the IFFT, a prefix which is simply all zeros is transmitted. This is illustrated in the example which shows three OFDM symbols 60,62,64 and a zero padded prefix before OFDM symbols 62 and 64. At the receiver, the OFDM ISIk−1 66 due to OFDMk−1 60 will occur in the zero-padded prefix of OFDM symbol 62. Similarly, the OFDM ISIk 68 due to OFDM symbol 62 will occur during the zero-padded prefix for symbol OFDMk+1 64. An advantage of this method is that the power wasted in the previous method is saved. However, the bandwidth occupied by those zeros is still a pure overload.